Abstract : Whereas it is relatively easy to account for the formation of concentric (target) waves of cAMP in the course of Dictyostelium discoideum aggregation after starvation, the origin of spiral waves remains obscure. We investigate a physiologically plausible mechanism for the spontaneous formation of spiral waves of cAMP in D. discoideum. The scenario relies on the developmental path associated with the continuous changes in the activity of enzymes such as adenylate cyclase and phosphodiesterase observed during the hours that follow starvation. These changes bring the cells successively from a nonexcitable state to an excitable state in which they relay suprathreshold cAMP pulses, and then to autonomous oscillations of cAMP, before the system returns to an excitable state. By analyzing a model for cAMP signaling based on receptor desensitization, we show that the desynchronization of cells on this developmental path triggers the formation of fully developed spirals of cAMP. Developmental paths that do not correspond to the sequence of dynamic transitions no relay-relay-oscillations-relay are less able or fail to give rise to the formation of spirals.
Abstract : The factors affecting the period are examined in a model for circadian oscillations of the period protein (PER) in Drosophila. The model for the circadian clock is based on multiple phosphorylation of PER and on the negative feedback exerted by PER on the transcription of the period (per) gene. The results are used to address the possible bases of the relative invariance of the period of oscillations with respect to temperature. Such a phenomenon, referred to as temperature compensation, represents one of the most conspicuous properties of circadian rhythms.